Pierre-Louis Lions

Pierre-Louis Lions
Philippe Binant · CC BY-SA 3.0 · source
Name	Pierre-Louis Lions
Birth date	11 March 1956
Birth place	Grasse, Alpes-Maritimes, France
Nationality	French
Field	Mathematics
Institutions	École Normale Supérieure (Paris), Université Paris-Dauphine, Université de Paris, Collège de France, Centre national de la recherche scientifique
Alma mater	École Normale Supérieure (Paris), Université Paris-Sud
Doctoral advisor	Jacques-Louis Lions
Doctoral students	Hugo Duminil-Copin, Nicolas Fournier
Known for	Viscosity solutions, Hamilton–Jacobi equations, kinetic theory, mean-field limits
Prizes	Fields Medal

Contents

Pierre-Louis Lions (born 11 March 1956) is a French mathematician noted for foundational work in partial differential equations and mathematical analysis. His research has influenced Caltech, Princeton University, Massachusetts Institute of Technology, University of Cambridge, and numerous schools across France, United States, United Kingdom, and Japan. Lions received the Fields Medal for contributions that connected nonlinear analysis, probability, and applied mathematics.

Early life and education

Born in Grasse in the Alpes-Maritimes, Lions studied at institutions including École Normale Supérieure (Paris) and Université Paris-Sud. He completed doctoral work under Jacques-Louis Lions at University of Paris-Sud and gained early exposure to research communities in Paris, Lyon, and Grenoble. During his formative years he engaged with seminars at Institut des Hautes Études Scientifiques, interacted with researchers from CNRS, Collège de France, and attended conferences like the International Congress of Mathematicians and meetings organized by the American Mathematical Society and European Mathematical Society.

Lions held positions at French and international institutions including Université Paris-Dauphine, Université de Paris, and the Collège de France. He collaborated with researchers at École Polytechnique, Sorbonne University, University of California, Berkeley, Stanford University, New York University, Imperial College London, and ETH Zurich. His teaching and supervision connected him to doctoral programs at École Normale Supérieure (Paris), Université Paris-Sud, and graduate schools linked to CNRS and the Institut Henri Poincaré. Lions participated in editorial work for journals such as the Annals of Mathematics, Communications on Pure and Applied Mathematics, Journal of Differential Equations, and contributed to panels for funding agencies like the European Research Council and national bodies in France.

Lions made seminal advances in the theory of viscosity solutions for Hamilton–Jacobi equations, developing tools that influenced research in optimal control theory, stochastic processes, kinetic theory, and the analysis of nonlinear partial differential equations. His work on the existence and uniqueness of weak solutions linked to Boltzmann equation, Vlasov equation, and mean-field limits established bridges between deterministic PDE analysis and probabilistic interpretations in collaborations with researchers from Princeton University, University of Chicago, and École Polytechnique. Lions contributed to the theory of compensated compactness drawing on interactions with scholars at Indiana University and University of Minnesota, and influenced numerical analysis approaches used at INRIA and Los Alamos National Laboratory.

He developed methods applied to problems associated with the Navier–Stokes equations, conservation laws studied by groups at Brown University and University of Oxford, and control problems addressed at California Institute of Technology and University of Toronto. His contributions to homogenization theory connected with work at University of California, Los Angeles and University of Wisconsin–Madison. Lions’ interdisciplinary reach affected research in statistical mechanics and mean-field games linked to contemporary studies at University of Warwick and Bocconi University.

Lions received the Fields Medal and was elected to prestigious bodies including the Académie des sciences and international academies. He earned prizes recognizing achievements in analysis and applied mathematics from organizations such as the European Mathematical Society and national French honors associated with Ordre national du Mérite and distinctions granted by CNRS. He delivered plenary talks at the International Congress of Mathematicians and received invitations to lecture at institutes including Institute for Advanced Study, Mathematical Sciences Research Institute, and Kavli Institute for Theoretical Physics.

Selected works include influential papers and monographs on viscosity solutions, kinetic equations, and nonlinear PDEs published in venues such as Annals of Mathematics, Communications on Pure and Applied Mathematics, and collections from the American Mathematical Society. Notable collaborative publications involved coauthors from Université Paris-Dauphine, École Normale Supérieure (Paris), University of Cambridge, and Princeton University. His doctoral students have taken positions at institutions including École Polytechnique, Université Paris-Sud, University of Geneva, ETH Zurich, and Harvard University.

Category:French mathematicians Category:Fields Medalists